In mathematics, a Galois extension is an algebraic field extension E/F that is normal and separable; or equivalently, E/F is algebraic, and the field fixed ... Characterization of Galois... · Examples

1 июл. 2016 г. · Let L,K be fields with L/K a field extension. We say L/K is a Galois extension if L/K is normal and separable. Galois extension is (not) transitive - Mathematics Stack Exchange Are all Galois extensions simple? - Math Stack Exchange Другие результаты с сайта math.stackexchange.com

1. K is the splitting field for a collection of separable polynomials. When K is a finite extension, then only one separable polynomial is necessary.

A field extension E/F is called Galois if it is algebraic, separable, and normal. It turns out that a finite extension is Galois if and only if it has the “ ...

5 февр. 2010 г. · Classically, “Galois extension” refers to a class of extensions of fields. An extension K ⊂ L K\subset L of fields is Galois if it is normal ...

Galois extension of the field K. Definition 2. A field P is a Galois extension of its subfield K if there exists a finite group G of automorphisms of the field ...

In mathematics, the fundamental theorem of Galois theory is a result that describes the structure of certain types of field extensions in relation to groups.

Crossed products are examples of Hopf Galois extensions. The definition of these extensions has its roots in the Chase, Harrison and Rosenberg.

25 нояб. 2023 г. · An extension of a field that is algebraic, normal and separable. The group of all automorphisms of a Galois extension K/k that leave all ...